The Department of Energy gave final approval yesterday to a $3 billion liquefied natural gas project designed to bolster California's lagging gas supplies with fuel to be shipped from Alaska and Indonesia.

Except for a few details, the decision ends a six-year struggle by California's two biggest natural gas distributors to negotiate a particularly complex maze of federal red tape and win permits for the project.

The DOE order would permit construction of a $618 million terminal at Little Cojo Bay near Point Conception in California's Santa Barbara County. At the terminal, the liquid gas would arrive by ship from Alaska and Indonesia, be regasified to its original volume and then distributed to customers throughout California by Pacific Gas and Electric Co. of San Francisco and Pacific Lighting Corp. of Los Angeles.

The remaining minor decisions are expected to be made by another agency, the Federal Energy Regulatory Commmission, within the next several weeks. Unless there are court delays caused by the project's opponents, the gas companies should be able to keep to their goal of completing design work during the coming year and breaking ground at Point Conception in late 1980. Operation would start in late 1983 or early 1984.